please help me ! :(

Question

How high must the gauge pressure in a fire hose be if the fire hose is to spray water to a height of 21 m?   (The density of water is 1000 kg/m³)

Answer 1

Let

h = 21 m he the desired height,

d = 1000 kg/m³ be the density of water,

g = 9.81 m/s² be gravitational acceleration,

p (to be calculated) be the pressure in the hose.

We are going to use conservation of energy.

The potential energy of the water at height h comes from its pressure energy in the hose.

Consider a small volume V of water.

Its mass is

m = Vd

Its pressure energy is pV.

Its potential energy at height h is mgh.

Conservation of energy gives the equation

pV = mgh

p = mgh/V = dgh = 1000×9.81×21 = 206,000 N/m² ≈ 2 atm